To solve the quadratic equation x² + 2x + 3 = 0, we can use the quadratic formula, which is given by:
x = (-b ± √(b² – 4ac)) / 2a
Here, a = 1, b = 2, and c = 3. First, we need to calculate the discriminant, b² – 4ac:
– Calculate b²: 2² = 4
– Calculate 4ac: 4 * 1 * 3 = 12
– Now, compute the discriminant: 4 – 12 = -8
Since the discriminant is negative, this means that the equation has no real solutions. However, we can find the complex solutions.
Now, substituting the values into the quadratic formula:
x = (-2 ± √(-8)) / 2(1)
We can simplify this further:
x = (-2 ± 2i√2) / 2
Breaking this down:
x = -1 ± i√2
Thus, the solutions to the equation x² + 2x + 3 = 0 are:
x = -1 + i√2 and x = -1 – i√2